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EXPERIMENTAL STUDY ON BINARY DROPLET

EVAPORATION AT ELEVATED PRESSURES

AND TEMPERATURES

HOJAT GHASSEMI*SEUNG WOOK BAEKQASIM SARWAR KHAN

Division of Aerospace Engineering, Departmentof Mechanical Engineering, Korea Advanced Instituteof Science and Technology, Yusung-Gu, Taejon, Korea

The evaporation characteristics of single and multicomponent

droplets hanging at the tip of a quartz fiber are studied experimen-

tally at the different environmental conditions under normal gravity.

Heptane and Hexadecane are selected as two fuels with different

evaporation rates and boiling temperatures. At the first step, the

evaporation of single component droplet of both fuels has been exam-

ined separately. At the next step the evaporation of several blends of

these two fuels, as a binary component droplet, has been studied. The

temperature and pressure range is selected between 400 and 700�C,

and 0.1 and 2.5 MPa, respectively. A high-temperature environment

was provided by a falling electrical furnace. The initial diameter of

droplet was in the range of 1.1 and 1.3 mm. The evaporation process

was recorded by a high-speed CCD camera. The results of binary

droplet evaporation show the three-stage evaporation. In the first

stage the more volatile component evaporates. The droplet tempera-

ture rises after an almost non-evaporative period and, in the third

stage, a quasi-linear evaporation takes place. The evaporation of the

binary droplet at low pressure is accompanied with bubble formation

Received 31 January, 2005; accepted 28 June, 2005.

The present work was supported by the Combustion Engineering Research Center at

the Department of Mechanical Engineering, Korea Advanced Institute of Science and

Technology, which is funded by the Korea Science and Engineering Foundation.�Address correspondence to [email protected]

Combust. Sci. and Tech., 178: 1031–1053, 2006

Copyright Q Taylor & Francis Group, LLC

ISSN: 0010-2202 print/1563-521X online

DOI: 10.1080/00102200500296697

1031

and droplet fragmentation and leads to incomplete microexplosion.

The component concentration affects the evaporation behavior of

the first two stages. The bubble formation and droplet distortion does

not appear at high environment pressure.

Keywords: liquid droplets, multicomponent droplet, droplet evapor-

ation, microexplosion

INTRODUCTION

Vaporization of a liquid fuel droplet at high pressure and high tempera-

ture environments is one of the basic mechanisms in spray combustion

for various applications such as industrial furnaces, gas turbines, diesel

engines, and liquid propellant rocket engines. The study of evaporation

of a single droplet is necessary for characterizing and understanding

spray vaporization and combustion. In many applications, droplets

consist of a mixture of two or more pure liquids. The multicomponent

droplets may consist of several species with completely different physical

and chemical properties. The degree of volatility, boiling temperature,

evaporation latent heat, surface tension, and heat capacity of each

component play an important role in the interior thermo-fluid dynamics

of droplet. There are various complications that occur during vaporiza-

tion of multicomponent liquid droplets. Different components vaporize

at different rates, creating concentration gradients within droplets and

causing mass diffusion. Also, evaporation of components with relatively

low boiling temperature produces vapor, forms vapor bubbles and causes

temperature and concentration gradients inside the droplets. In some

cases, pressure buildup in bubbles leads to complete or incomplete

explosion of droplets.

The evaporation characteristics of multicomponent droplets have

been studied [e.g., Law, 1978; Randolph et al., 1986; Arias-Zageti and

Rosner, 2003; Morin et al., 2004] analytically and experimentally.

Concentration and thermodynamic properties of species play very sig-

nificant roles in evaporation of binary or multicomponent droplets.

The evaporation of the more volatile component, due to its lower boiling

temperature, produces bubbles within the droplet and leads to a micro-

explosion. Disruptive boiling or microexplosion is possible, because

for certain regions of the droplet interior, the equilibrium vapor pressure

of the more volatile component can exceed the ambient pressure

1032 H. GHASSEMI ET AL.

(Sirignano, 1999). The examinations of several n-paraffin fuels in a wide

range of concentrations as the binary fuel have shown that for occur-

rence of disruption, a minimum difference in the normal boiling points

of components, as well as a certain initial concentration of the more

volatile component, must exist (Lasheras et al., 1980). Previous experi-

mental results on two component fuels substantiates a three-staged

evaporation and combustion (Wang et al., 1984). The three-staged

evaporation confirms that the diffusion is the dominant transport

mechanism in droplets. They also have shown that the occurrence of

microexplosion depends sensitively on component concentration. Law

(1982) presented a good review on vaporization and combustion of

droplets.

To study of some characteristics of binary droplet evaporation, sev-

eral mixtures of normal heptane and normal hexadecane have been

examined. The evaporation of each component has been studied at

normal gravity condition and different environmental pressures and

temperatures as a single component fuel, separately. In this study,

the environment pressure has varied from atmospheric pressure to

2.5 MPa. The environment temperature range from 400 to 700�C.

Experiments were performed with an individual droplet suspended at

the tip of quartz fiber. The initial diameter of droplets ranged between

1.1 and 1.3 mm. The evaporation rate has been expressed as the time

derivative of droplet diameter squared. This coefficient can be extracted

from the linear part of the evaporation history curve. The evaporation

history is achieved by examination of temporal droplet diameters

obtained using a high-speed camera.

The effects of temperature and pressure on evaporation rate have

been studied for single components as well as binary component dro-

plets. The evaporation of a binary droplet does not follow the single

component droplet evaporation, instead showing a three-staged beha-

vior. Examination of several component concentrations in a binary drop-

let shows the three-staged feature of evaporation history does not change

significantly. Under low pressure conditions, the evaporation of a binary

droplet leads to bubble formation within the droplet after a short heating

and linear evaporation period. The fast motion of bubbles causes high

distortion in the droplet shape and finally leads to the rupture of bubbles,

fragmentation and incomplete explosion of droplets. High-speed record-

ing of the evaporation process shows this phenomenon takes place

several times in a relatively long period.

BINARY DROPLET EVAPORATION AT ELEVATED P, T 1033

EXPERIMENTAL SETUP

A schematic of the experimental apparatus is shown in Figure 1.

A droplet hanging on a fine quartz fiber with 0.125 mm diameter was

subjected to the hot environment by a freely falling furnace, thereby

resulting in evaporation. This unit is enclosed within a high pressure

vessel installed with glass windows that enabled us to observe the

evaporation process using a high speed camera. Due to a flexible feature

Figure 1. A sketch of experimental setup. (1) Pressure vessel, (2) guide bar, (3) furnace

entrance, (4) electric furnace, (5) quartz glass window on furnace, (6) temperature control-

ler, (7) lever, (8) nitrogen vessel, (9) quartz glass window on pressure vessel, (10) backlight

source, (11) quartz fiber, (12) droplet, (13) shock absorber, (14) droplet maker, (15) plunger

micro pump, (16) CCD camera.


of the furnace design, the ambient gas temperature steps up from low to

high stage in a short time. Thus, the heat leakage from furnace to outside

is negligible. Also, since a thin quartz fiber is used for droplet suspen-

sion, the heat transfer between droplet and fiber is minimized. The

detailed description of the experimental setup, levels of accuracies, and

procedure can be found in Ghassemi et al. (2005).

TEST MATRIX

To study of some characteristics of binary droplet evaporation, several

blends of two pure hydrocarbons have been examined. Normal heptane

as a very high volatile fuel and normal hexadecane as a very low volatile

fuel have been selected with normal boiling temperature 98�C and 287�C,

respectively. To find a clear picture of binary droplet evaporation, the

evaporation of each main component has been studied as a single

component droplet, separately. Droplet component concentrations for

several mixtures of these fuels are shown in Table 1.

Evaporation of a single droplet, which is hanged on tip of a quartz

fiber, has been studied at several environments. The environment press-

ure has varied from atmospheric pressure to 2.5 MPa in 0.5 MPa incre-

ments. The environment temperature covers from 400 to 700�C by

100�C.

The critical pressures of normal heptane and normal hexadecane

are 2.74 and 1.55 MPa, respectively. Also, the critical temperatures

for these fuels are 276 and 451�C, respectively. The pressure range

includes the critical pressure of hexadecane. Therefore, in this study,

evaporation of heptane droplets takes place at subcritical conditions.

Oppositely, the temperature range is beyond the critical temperature

of heptane.

Table 1. Droplet compositions (vol. %)

Mixture Heptane Hexadecane

1 100 0

2 70 30

3 50 50

4 30 70

5 0 100


DATA REDUCTION

Time histories of evaporation process are recorded on a personal

computer via a high speed camera. Several recording speeds were

examined. Comparison of evaporation coefficients obtained on several

cases did not show a significant difference for 30, 100, and 200 frames

per second. In the cases with low evaporation rate, 30 frames per second

was selected for image recording speed, whereas in the cases of high

evaporation rate, 200 frames per second was used. To record the

partially microexplosion, 500, 1000, and 2000 frames per second were

used. A flexible image-processing program has been developed to extract

droplet shape and size. The resolution of each image in horizontal and

vertical direction was 1158 dpi. Using high-resolution image diminishes

the error in droplet size extraction via image processing.

Uncertainty in determination of droplet diameter comes from two

sources. One is the scale factor, which is used to convert the droplet

diameter size in pixels to real units (mm). An opaque needle with a

known diameter is used as reference scale. At the worst case, the mea-

surements in wide range of light intensities show that error is less than

�0.05 mm. Another source for error in measuring droplet diameter is

due to optical effect of hot and dense environment. At high pressure

and high temperature, fuel vapor surrounds the droplet so that a deter-

mination of droplet boundary incurs some difficulty, because a density

gradient around droplet would produce mass diffusion and make poor

visibility condition. Using a least square regression in calculation of

evaporation rate from instantaneous diameter trajectories would mini-

mize this sort of error.

Figure 2 depicts a sample of droplet evaporation history. It shows the

square of droplet diameter versus time for n-Heptane droplet vaporization

at 2.0 MPa and 700�C. The initial diameter of droplet is 1.285 mm.

This curve is composed of two completely different sequences. The first

sequence shows a non-linear behavior while the second one shows a linear

regression in squared diameter. In the first or heat up period, the diameter

of droplet increases and after some times starts to decrease. This behavior

in droplet is due to its heat-up by thermal conduction from gas and sub-

sequent thermal expansion. As temperature of droplet surface increases

and reaches its boiling temperature, evaporation starts. After that, a

balance between thermal expansion and evaporation determines diameter

of droplet. When the temperature inside the droplet reaches a quasi steady


state, only evaporation is effective on the determination of droplet size.

From this stage, the d2-law evaporation is valid. For the case shown in Fig-

ure 2, the maximum increment of squared diameter, ðDd2Þmax, is about 6%

in relation to initial squared diameter, which corresponds to 3% in

diameter.

In Figure 2, the lifetime of droplet has been divided into two parts; t0indicates the nonlinear behavior part and the remainder is related to

d2-law evaporation. For the purpose of evaporation study, t0 does not

have importance, because the evaporation rate is determined by the

second part of droplet behavior. For the study of ignition and combus-

tion of droplets, however, t0 is an important characteristic of large liquid

fuel droplet. The behavior of t0 is a function of initial droplet size, tem-

perature of environment, and composition of droplet. Based on mass flux

of the evaporating liquid droplet (Forhan and Roth, 1999) for a small

droplet, which heat-up period is negligible, d2-law is expressed as

d2 ¼ d20 � Cvt, where Cv is the evaporation rate (evaporation coefficient)

and d0 is the initial droplet diameter. As indicated in Figure 2, the evap-

oration rate can be expressed as the time derivative of droplet squared

Figure 2. Temporal variation of the square of droplet diameter.


diameter, Cv ¼ �dðd2Þ=dt. This coefficient can be extracted from the lin-

ear part of the evaporation history curve. The slope of this line, which is

passing through the second part, is the minus of evaporation rate. The

best-fit straight line can be calculated using the least square regression.

Experimental study of a single droplet, which is suspended at the tip

of a quartz fiber, encounters two additional effects. Heat conduction from

quartz fiber into droplet and radiative heat transfer from the furnace wall

introduce extra heat feedback to the droplet. The effect of heat conduction

through the supported fiber has been investigated experimentally and

theoretically (e.g., Yang and Wong, 2002; Wong and Lin, 1992). A general

conclusion is that heat conduction through quartz fiber enhances evapor-

ation. The effect is strange when environment temperature is low and the

fiber thickness is high. In the present study, using a thin quartz fiber in a

hot environment minimizes the effects of heat conduction into the droplet.

Although the effect of conducted heat through the suspending fiber

becomes significant in the ending part of droplet lifetime.

The effect of radiative heat transfer from the furnace wall into the

droplet has been also studied (Kadota and Hiroyasu, 1976) using an ana-

lytical model. A combination of radiative effect and heat conduction

through the fiber can decrease the lifetime of the droplet dramatically.

In the specific case of using n-heptane droplet in a nitrogen-filled

environment at 500�C and 3.0 MPa, the lifetime of the droplet was

reduced by about 15%. In the present study, the ceramic shields cover

the electrical elements, which are installed in the furnace walls. The

shields prevent the direct radiation of electrical elements at high tem-

perature and reduce the wall temperature as close as possible to the

desirable temperature. Therefore, using a shielded heating element would

decrease the radiative effects on droplet.

RESULTS AND DISCUSSIONS

Single Component Droplet Evaporation

General Behavior. Figure 3 shows variations of normalized squared

diameter with the normalized time for different environment temperatures

and constant pressure 1.0 MPa for n-heptane and n-hexadecane. Each

evaporation history follows the same general behavior. After a finite

heating-up period, the variation of square of droplet diameter becomes

approximately linear with time, while keeping d2-law at the last stage.


A little deviation from d2-law evaporation has been detected at lower tem-

perature (400�C) in hexadecane evaporation. This general behavior has

been also observed in evaporation at different environment pressures. As

depicted in this figure increasing in ambient temperature decreases the

total lifetime of droplets of heptane and hexadecane. Also, heptane dro-

plets show shorter lifetime than hexadecane.

In Figure 4 the normalized time history of diameter squared of droplet

at different ambient pressure and constant temperature 700�C has been

Figure 4. Variations of normalized diameter (squared) with the normalized time for several

environment pressures at 700�C for (a) heptane and (b) hexadecane.

Figure 3. Variations of normalized diameter (squared) with the normalized time for several

environment temperatures at 1.0 MPa for (a) heptane and (b) hexadecane.


shown. The evaporation at different pressure shows different droplet life-

time for heptane. While in the case of hexadecane, different environment

pressures do not show significant effect on droplet lifetimes.

At the low temperature, evaporation of hexadecane droplets is not

completely linear. In Figure 5, time histories of diameter squared for

hexadecane droplets at 400�C and various ambient pressures are shown.

As this figure shows, after a heating-up period, instead of showing a con-

stant rate according to d2-law, evaporation, take place at variable rate.

When the ambient temperature, related to the fuel boiling temperature,

is not too high, temperature within the droplet is not uniform. Therefore,

temperature near the vaporizing surface is not too close to boiling tem-

perature. When temperature distribution within the droplet is taken into

account, the evaporation does not follow the d2-law. But in the end phase

the droplet temperature is almost uniform. Therefore the evaporation is

approximately linear and follows the d2-law. Values of evaporation rates

at 400�C that are shown in the following figures are obtained from the

nearly linear part of evaporation.

Effects of Temperature. The effects of ambient temperature on the evap-

oration rates of heptane and hexadecane have been investigated under dif-

ferent environmental pressures. A simple comparison of evaporation rates

of heptane between previous results of Sato (1993) and current study at

Figure 5. Temporal variations of diameter (squared) of hexadecane droplet for several

environment pressures at 400�C.


1.0 MPa pressure has been made in Figure 6a. As this figure shows, despite

leak of data at low temperatures in current study and at high temperatures

in results of Sato (1993), the evaporation rates confirm each other in both

trend and value.

The variations of evaporation rates of Heptane in terms of environ-

mental temperature have been depicted in Figure 6b. As the ambient

temperature is increased, the evaporation rate monotonically increases.

This trend is held for different environment pressures. In Figure 6c the

effects of temperature on evaporation rate are shown for different

environmental pressures for hexadecane. As indicated in this figure,

the evaporation rate increases, versus temperature, monotonically.

Figure 6. Effects of ambient temperature on the evaporation rate; (a) a simple comparison

of the evaporation rate of heptane between and current studies Sato (1993), (b) the evap-

oration rate of heptane and (c) hexadecane at different ambient pressures.


The dependency of evaporation rate of hexadecane on temperature is

strong when the ambient pressure is higher than the critical pressure.

Effects of Pressure. Figure 7a shows variation of the evaporation rate

versus ambient pressure for heptane droplets. The evaporation rate

shows a monotonic manner at all environment temperature. This figure

shows also the evaporation rate may take a maximum at pressure slightly

greater than 2.5 MPa. As indicated in this figure, the ambient pressure at

which the evaporation rate may reach to a maximum increases as the

ambient temperature increases. Actually, the critical pressure of heptane

is 2.74 MPa and according to the previous works (e.g., Sato, 1993) evap-

oration rate of Heptane takes a maximum around the critical pressure.

Figure 7b shows the dependency of the evaporation rate to the ambi-

ent pressure at different temperatures. When the ambient temperature is

low (400�C) the evaporation coefficient decreases and reaches to a mini-

mum, then increases with the ambient pressure. At the intermediate

ambient temperatures (500 and 600�C), where it is around the critical

temperature of hexadecane, the evaporation coefficient does not take a

minimum. It decreases monotonously, at least in the working pressure.

It may take a minimum at higher pressure. Actually, the evaporation rate

at the above mentioned environment temperature does not change too

much. When the ambient temperature is sufficiently above the critical

temperature of hexadecane, the evaporation rate increases with pressure

and takes a maximum at pressure slightly greater than critical pressure.

Figure 7. Variations of the evaporation rate versus ambient pressure at several ambient

temperatures for (a) heptane and (b) hexadecane.


Binary Component Droplet Evaporation

General Behavior. The general behavior of the binary droplet evapor-

ation process is completely different from a single component droplet.

Figure 8 represents two samples of normalized diameter squared histories

for binary droplets. One curve shows the droplet history at atmospheric

pressure while the other shows evaporation at elevated environment

pressure. Both curves show three-staged evaporation of a binary droplet.

The evaporation of binary droplet at low pressure is accompanied with

bubble formation within the droplet. This leads to highly distortion of

droplet shape. But due to high external pressure, bubble formation or

its demonstration does not take place.

Bubble formation, distortion and partial rupture of droplets take

place with different strengths at different ambient temperatures. When

the temperature increases, the strength also increases. A comparison

of droplet histories during vaporization for different environment tem-

peratures is shown in Figure 9. At low temperature, the droplet distor-

tion is not too strong, but bubble formation and rupture take place

several times. Before each rupture, the droplet diameter increases due

to bubble expansion inside.

Evaporation of heptane, which is uniformly mixed in the droplet

composition at the beginning, takes place at lower temperatures than

the hexadecane. When droplet senses a high-temperature environment,

Figure 8. The general binary droplet diameter (squared) history for evaporation at low and

high pressure environments.


the temperature within the droplet reaches to the boiling temperature of

heptane. At the same time, the temperature is less than the boiling tem-

perature of hexadecane.

Heptane that is near the droplet surface, vaporizes quickly and leaves

the droplet surface easily. The heptane that are in region far from droplet

surface, also reach to the boiling temperature but they cannot leave the

droplet as easily as in the beginning. Because hexadecane that is surround-

ing the droplet, does not evaporate yet and also its surface tension is

enough high to prevent the heptane vapor escape. The vapors are trapped

in the droplet from a bubble. As heptane evaporates more, the pressure

inside of bubble builds up and causes the dilation of droplet. When the

bubble pressure reaches to appropriate value, the bubble bursts and hep-

tane vapors leave the droplet. These local ruptures take place at the outer

region of droplet, therefore the complete microexplosion does not appear.

At the higher environment temperature, heat diffusion into droplet is

faster than the lower one. Therefore the inside droplet temperature,

quickly, reaches to the boiling temperature of heptane. It leads to fast

vapor formation inside of droplet, while the hexadecane starts to evapor-

ate. Therefore, the heptane vapors leave along with tiny fragments of

hexadecane easily.

The outward motion of bubbles makes a very strong internal flow

inside the droplets. This fact has been observed by high speed

Figure 9. Comparison of binary droplet evaporation histories at low pressure and different

environment temperatures.


photography. The movie shows a rotational dislocation of bubbles with

high frequency. The break-open of bubbles is accompanied with incom-

plete fragmentation of droplet.

After some time, most of heptane leaves the droplet and this dyna-

mism disappears gradually. It is important to note that when heptane

completely leaves droplet, the normalized diameter squared should reach

to 0.63. As indicated in Figure 8, droplet distortion has disappeared

before. A little difference, which is shown by D(d2=d02), may come from

dead volume of the quartz fiber and its tip bead.

In Figure 10, several frames of droplet photograph during evapor-

ation at atmospheric pressure and 600�C have been shown. The first

photo (top left) shows droplet at the beginning of evaporation. The

second one shows slight distortion in droplet shape, which indicates

the bubble formation inside the droplet. Other frames show very large

deformations in droplets. They also show some fragments that leave

the droplet. These fragments consist of liquid hexadecane and some

heptane vapor that is trapped in. The last frame (bottom right) shows

a photograph of droplet after irregular deformation has been finished.

In Figure 11 the normalized time histories of squared diameter of

droplet at different ambient conditions have been shown. Figure 11a

Figure 10. Some sequential photographs of droplet vaporization under low ambient

pressure.


presents evaporation history at ambient pressure 1.0 MPa and different

temperatures. The lifetime and evaporation rate of droplet extremely

vary at different temperature. In other hand, as shown in Figure 11b,

the effect of pressure on evaporation process is not too strong. This

figure emphasizes that the bubble formation and probably explosion of

droplet is suppressed when environment pressure increases. But previous

experimental study of binary droplet explosions with different compo-

nent confirms the enhancement of the occurrence of microexplosion

with increasing environment pressure (Wang and Law, 1985).

The evaporation history consists of three stages; a fast reduction in

droplet diameter in a relatively short period, a nearly non-evaporating

short period, and another period with diameter decay. In the first stage

the droplet senses the temperature rise and the temperature of high

volatile component (heptane) reaches to its boiling temperature earlier

than low volatile component (hexadecane). Heptane on and near the

droplet surface vaporizes, leaves the droplet and therefore the droplet

becomes smaller.

In the beginning of the second stage, the heptane, which was near

the droplet surface, has vaporized, resulting in a strong concentration

gradient with in the droplet. While the hexadecane is still in the heating-

up period, it does not start to evaporate. Therefore a mass diffusion

mechanism handles heptane to droplet surface. During mass diffusion,

there is not considerable evaporation. Thus the droplet size remains

almost constant, but the droplet temperature is going to increase and

also heptane is coming to droplet surface region.

Figure 11. Temporal variation of diameter (squared) of droplet for binary fuel at (a) different

temperatures and constant pressure, (b) different pressures and constant temperatures.


At the third stage, remainder of droplet vaporizes as the same

manner as the first stage. The well-mixed hexadecane and heptane drop-

let with a completely different composition from the initial, vaporizes as

a light-mixture binary droplet. The evaporation of remainder heptane

takes place before the droplet reaches end of lifetime. Actually, when

the evaporation rate is too slow, at the end period of the third stage,

the droplet contains hexadecane.

As shown in Figures 11a and b, when the evaporation rate is rela-

tively high, like at high temperature, the difference between two stages

is not too clear. Especially at 700�C and above 1.0 MPa pressure, the first

and third stages merge to each other and it is not possible to distinguish

three-staged evaporation. In other words, the duration of the second

stage diminishes. The three-staged evaporation has been also addressed

by other researcher (e.g., Wang et al., 1984). They have mentioned the

relative durations of these three stages must depend on the concentra-

tions of component. The effects of component concentration have been

discussed in the following section.

As mentioned previously, the three-staged evaporation of binary

droplet at low environment pressure is accompanied with bubble forma-

tion and its consequent phenomena. Unlike of evaporation at low press-

ure, escape of vapor from droplet does not lead to bubble formation

or droplet rupture. Because as pressure increases, surface tension of

hexadecane decreases and allows vapor to leave the droplet. The vapor-

ization of lighter component absorbs heat and increases the total heat

transfer resistance within the droplet. These lead to a delay for rising

of droplet temperature. Approximately two thirds of heptane vaporizes

and leaves the droplet in the first stage. This amount is calculated based

on the diameter squared at the end of this stage.

Effects of Temperature and Pressure. The evaporation rates of binary

droplet have been extracted from the linear part of the third stage evap-

oration history curves. Based on the above discussion, the evaporation

rate of binary droplet should follow the hexadecane. In Figure 12, a com-

parison between evaporation rate of hexadecane and binary fuel has been

presented. Figure 12a shows the effect of environment temperature on

evaporation of hexadecane and binary fuel at two low environment pres-

sures. The evaporation trend of the binary fuel is the same as hexadecane

but the lower rates. In Figure 12b the effect of environment pressure

on evaporation rates of the two fuels is compared. This figure also

emphasizes that the effect of pressure on evaporation rates of two fuels,


follows the same manner. The evaporation rate of binary fuel is almost

lesser than hexadecane evaporation rate. It is due to occupation of drop-

let atmosphere by vapors of more volatile fuel (heptane). The tempera-

ture of heptane vapors is lower than hexadecane. This relatively cold

gas decreases the total heat transfer from environment to the droplet.

Consequently, evaporation of droplet takes place at slower rate than pure

hexadecane.

Effects of Component Concentration. In the previous sections, the

evaporation of a 50% mixture of heptane and hexadecane as a binary

component droplet is described. According to Table 1, three combina-

tions of these fuels were selected to study the effects of component

concentration on evaporation of binary droplets. To achieve a clear

description, evaporation of single component droplet (pure heptane

and pure hexadecane) as two extremes of binary component is taken

into account. Since vaporization of the binary component droplets fol-

lows the three-staged behavior, the component concentration affects

the characteristics of the evaporation stages. Figure 13 shows the nor-

malized time histories of squared diameter of the droplet at 600�C for

different component concentrations. Figure 13a shows the evapor-

ation histories under atmospheric pressure, which is accompanied

with fragmentation of binary droplets. As it mentioned above, frag-

mentation of the binary droplet under high pressure does not appear.

Figure 12. Comparison between the evaporation rate of hexadecane and the binary fuel;

(a) effect of temperature and (b) effect of pressure.


Figure 13b shows the evaporation histories of binary droplets in high

pressure ambient.

In Figure 13a, curves A and E show the evaporation histories of

pure hexadecane and pure heptane droplets, respectively. During the

first stage of evaporation of binary droplet, two simultaneous events take

place. The first one is the evaporation of more volatile component

(heptane) causing reduction in droplet size and the other is heating of

less volatile component (hexadecane) resulting in thermal expansion of

droplet. For the droplets containing more volatile component in minor

proportion, like case B in Figure 13a, heating and evaporation of heptane

and heating of hexadecane consume the incoming heat. In competition

between droplet size reduction due to evaporation of heptane and

thermal expansion of hexadecane, the droplet diameter does not change

significantly. In the case of pure hexadecane droplet, curve A, all

incoming heat just heats the droplet and expands its diameter. That is

why in the case B, the droplet diameter remains nearly constant, and

droplet life time is longer than case A. As heat penetrates more into

droplet, more heptane evaporates and forms bubble inside the droplet.

The bubble breaking open causes the droplet fragmentation, as shown

in case B in Figure 13a. In high ambient pressure and in contrast with

the atmospheric pressure, the droplet size reduction due to evaporation

of Heptane overcomes to the thermal expansion of hexadecane. As

depicted in Figure 13b, curve B does not show a plateau in evaporation

Figure 13. Temporal variation of diameter squared of droplet for different binary fuels at

(a) low and (b) high pressure temperatures.


history. It is due to higher evaporation rate of heptane under high

pressure (See Figure 6b or Figure 7a). In the third stage, when nearly

all the heptane has vaporized and left the droplet, remainder histories

show a linear behavior. The remainder fuel at this stage is almost less

volatile component (hexadecane). The rate of evaporation in this stage

is lesser than the evaporation rate of pure hexadecane droplet at the

same ambient.

For the droplets containing more volatile component in major pro-

portion, like case D in Figure 13, the evaporation of heptane is the domi-

nant phenomenon at the first stage. The initial dilation of droplet due to

thermal expansion does not appear and the first stage evaporation fol-

lows the linear behavior in atmospheric and higher ambient pressure.

In case D, as shown in Figure 13a, bubble formation and incomplete

explosion exists with weak strength relative to cases B and C. After drop-

let fragmentation, the reminder of evaporation process becomes linear.

The evaporation rates in the first and third stages are lesser than the

evaporation rate of pure heptane droplets (case E) and pure hexadecane

droplets (case A), respectively. This is true in both low and high pressure.

In the first stage, the evaporation rate of a binary droplet (cases C and D)

is less than the evaporation rate of pure heptane, because of heat absorp-

tion by hexadecane within the droplet. In the third stage it is due to lower

heat transfer rate to the droplet from ambient temperature. In this case,

the relatively cold vapor of Heptane, which surrounded the droplet, acts

as an inhibitor.

A simple comparison between Figure 13a and b shows that if the

bubble formation does not occur, the lifetime of binary droplets, regard-

less to the composition, is shorter than the lifetime of less volatile

component. It confirms the bubble formation increases the total heat

resistance within the droplet. It means, the incoming heat into the drop-

let from outside regardless to its initial composition, cannot penetrate

into the inner part of droplet. The bubble not only increases heat transfer

resistance due to its very low heat conductivity, but also absorbs heat.

This heat absorption superheats vapor inside the bubble.

The general behavior of the evaporation of binary droplets with

different initial compositions at different ambient temperatures and pres-

sures are similar to that are discussed here. A detailed study on the effects

of component concentration on evaporation of binary droplets can be

found in Khan et al. (2005). A comparison between the evaporation

histories of binary droplets under atmospheric pressure and different


temperatures has been done. It is found that the bubble formation and

droplet fragmentation occurs when the droplet reaches a new compo-

sition. As indicated in cases C and D in Figure 13a, the fragmentation

happens when some part of more volatile component (heptane) vaporizes

and leaves the droplet. At this time, the droplet diameter is known and

assuming no hexadecane vaporization, it is not to difficult to find the

new composition of each component in the droplet.

CONCLUSIONS

The focus of this work was on the study of evaporation of a binary compo-

nent droplet. Normal Heptane and normal Hexadecane were selected as

high and low volatile fuel, respectively. These fuels have very different

boiling temperature. The evaporation rates of each component have been

investigated under different environment pressures and temperatures,

individually. The collected form of the evaporation rate dependency on

the pressure and temperature is shown if Figure 14a and b for heptane

and hexadecane, respectively.

Three different blends of heptane and hexadecane were examined as

binary fuels. This study has provided a useful insight to evaporation of

binary droplets at different environmental conditions. The specific

results are following.

Figure 14. Dependency of evaporation rate on ambient pressure and temperature for pure

fuels; (a) heptane and (b) hexadecane.


. The evaporation of the binary droplet at very low ambient pressure

leads to extremely distortion and incomplete fragmentation of droplet.

This phenomenon takes place due to vaporization of fuel with very less

boiling temperature. Bubble formation within droplet and its blasting

causes droplet fragmentation. At higher environment pressure, where

it overcomes to bubble pressure and the surface tension of hexadecane

decreases, droplet explosion does not appear.

. Regarding to high difference between the boiling temperatures of two

components, there is a very strong internal motion inside of droplet. It

emphasizes the droplet is encountered with a quick internal mixing.

. The evaporation history of the binary droplet consists of two main

stages with two nearly linear rates. These two stages are separated with

an almost non-evaporating period. An appreciable amount of compo-

nent with lower boiling temperature evaporates quickly in the first

stage. It means the gas-liquid mass diffusion is the dominant mech-

anism in vaporization of the binary droplet at first the stage.

. The evaporation rate of the binary droplet at the third stage is lesser

than the evaporation rate of less volatile single component droplet.

. The component concentration affects the characteristics of three-

staged evaporation. It also controls the lifetime of the droplets.

. The bubble formation at atmospheric pressure increases the total heat

transfer resistance within droplet and absorbs additional heat, which

superheats the vapor inside.

. Total binary droplet lifetime is longer than the lifetime of single

component droplet at low pressure.

REFERENCES

Arias-Zugasti, M. and Rosner, D.E. (2003) Multicomponent fuel droplet vapori-

zation and combustion using spectral theory for a continuous mixture.

Combust. Flame, 135, 271–284.

Forhan, A. and Roth, N. (2000) Dynamics of Droplets, Springer, Berlin,

Chaps. 3, 6.

Ghassemi, H., Baek, S.W., and Khan, Q.S. (2005) Evaporation of Binary

Droplets at Elevated Pressure and Temperature. AIAA Paper 2005-353,

43rd Aerospace Sciences Meeting and Exhibit, Reno, Nevada.

Kadota, T. and Hiroyasu, H. (1976) Evaporation of a single droplet at elevated

pressures and temperatures. Bull. JSME, 19(138), 1515–1521.

Khan, Q.S., Baek, S.W., and Ghassemi, H. (2005) Effect of Component Concen-

tration on the Evaporation and Microexplosive Behavior of Multicomponent


Fuel Droplets, 6th World Conference on Experimental Heat Transfer, Fluid

Mechanics, and Thermodynamics, April 17–21, 2005, Matsushima, Miyagi,

Japan.

Lasheras, J.C., Fernandez-Pello, A.C., and Dryer, F.L. (1980) Experimental

observations on the disruptive combustion of free droplets of multicompo-

nent fuels. Combust. Sci. Technol., 22, 195–209.

Law, C.K. (1978) Internal boiling and superheating in vaporizing multicompo-

nent droplet. AICHE J., 24(4), 626–633.

Law, C.K. (1982) Recent advances in droplet vaporization and combustion. Prog.

Energy Combust., 8, 171–201.

Morin, C., Chauveau, C., Dagat, P., Gokalp, I., and Cathonnet, M. (2004) Vapori-

zation and oxidation of liquid fuel droplets at high temperature and pressure:

Application to n-alkanes and vegetable oil methyl esters. Combust. Sci.

Technol., 176, 499–524.

Randolph, A.L., Makino, A., and Law, C.K. (1986) Liquid-phase diffusion resist-

ance in multicomponent droplet gasification. Proc. Combust. Instit., 21, 601.

Sato, J. (1993) Studies on droplet evaporation and combustion in high pressures.

AIAA Paper 93-0813. 31st Aerospace Sciences Meeting and Exhibit, Reno,

Nevada.

Sirignano, W.A. (1999) Fluid Dynamics and Transport of Droplets and Spray,

Cambridge University Press, UK.

Wang, C.H. and Law, C.K. (1985) Microexplosion of fuel droplets under high

pressure. Combust. Flame, 59, 53–62.

Wang, C.H., Liu, X.Q., and Law, C.K. (1984) Combustion and microexplosion of

freely falling multicomponent droplets. Combust. Flame, 56, 175–197.

Wong, S.-C. and Lin, A.-C. (1992) Internal temperature distributions of droplet

vaporizing in high-temperature convective flow. J. Fluid Mech., 237, 671–687.

Yang, J.-R. and Wong, S.-C. (2002) An experimental and theoretical study of the

effects of heat conduction through the support fiber on the evaporation of a

droplet in a weakly convective flow. Inter. J. Heat Mass Trans., 45, 4589–4598.


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